Can someone show me how to solve this calculus problem?

Question

Answer 1

Favorite Answer

Corrected mistake and YA hid it (fix things) 

Answer 2

z = x^6ln[1 + xy^(-5/7)]

dz/dx = ln[1 + xy^(-5/7)] d/dx 6x^5 + x^6 d/dx 1/[1 + xy^(-5/7)] d/dx y^(-5/7)

..............................................x^6

=6x^5ln[1 + xy^(-5/7)] + ------------------------------ answer//

.........................................y^(5/7)[1 + xy^(-5/7)]

dz/dy = x^6* 1/(1 + xy^(-5/7)) d/dy -5/7xy^-12/7

......-5/7x^7

=------------------------------ answer//

...y^(12/7)(1 + xy^(-5/7)